The long-range aims of our research relate to the analysis of exposure- time-response relationships in epidemiologic studies, particularly those involving extended and time-varying exposure histories. Much of our work has also addressed the efficient design of sampling plans for nested case-control and case-cohort analyses of cohort studies. In this second continuation proposal, we are asking support to continue our work in this general area, with some changes in direction. Methods of exposure-time-response modeling: We plan to develop methods for describing exposure-response relationships for extended time- dependent exposure histories, taking into account the modifying effect of time-related variables such as age at exposure and latency. We will develop methods for fitting simple empirical models and stochastic models of carcinogenesis and pharmacodynamics, to epidemiologic data and for testing the goodness of fit. Alternative methods will be compared using computer simulation and applied to various data sets. Specific models would include the Armitage-Doll multistage and Moolgavkar-Knudson two- stage models, extensions of them for radiation carcinogenesis, and addition of simple kinetic models for tissue dose. We will explore the adequacy of certain approximations that are commonly used and compare the results with exact solutions, where available. Investigation of alternative approaches to the design and analysis of nested case-control and case-cohort studies: We propose to extend stratified and two-stage designs previously developed for unmatched case- control studies to matched designs. In the unmatched situation, it has been shown that great efficiency gains can be expected when assessing confounding and/or interactions. We will extend our previous work on nested case-control and case-cohort sampling to allow for stratified sampling. The basic idea in all of these designs is to improve the efficiency of the design by exploiting information on entry/exit times and covariates that is already available on the full cohort in selecting controls. The methods developed above will be illustrated by application to a number of data sets available to us. We are coinvestigators on a wide range of epidemiologic studies of cancer. A major substantive interest of the principal investigator is in the area of radiation carcinogenesis, and the above problems have arisen in a number of these studies, including the atomic bomb survivors, uranium miners, second cancers in radiotherapy patients, electromagnetic fields, and fallout from the Nevada Test Site. In addition, we plan to reanalyze data on lung cancer from several cohort and animal studies of smoking.